The England midfielder has been ruled out of Saturday's Premier League clash at Everton after falling in training.
Lambert is waiting to discover the extent of Delph's injury, which he fears may be a dislocated shoulder, and an operation may be needed to repair the damage.
When asked if Delph had suffered a dislocation, the Scot said: "Aye, [it's] probably that.
"Whether it is enough to allow it to rest for a couple of weeks I don't know or if there is more to it. I am pretty sure the medical people will discuss that.
"That's the thing, we don't know. That will be left up to the medical people to see what is the best procedure for it.
"It was an awkward fall. No-one was near him. He fell on his shoulder. It is not always straightforward so we need to go and get it checked out."
Villa will also be without defender Philippe Senderos (thigh) for the clash at Goodison Park.
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